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Roller Coaster Energy: Potential and Kinetic, Effects of Height and Separation, Exams of Acting

This document from LABScI at Stanford provides instructions for an experiment investigating the relationship between potential and kinetic energy in roller coasters. Students are asked to determine the maximum hill height for a marble by dropping it from various heights and measuring the resulting hill height. The document also explores energy dissipation through friction and the flexibility of the foam, and calculates the minimum velocity required for a marble to complete a loop. Conceptual questions ask about the location of potential and kinetic energy on a roller coaster and why the first hill is always the highest.

Typology: Exams

2021/2022

Uploaded on 09/27/2022

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Created by LABScI at Stanford
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Potential and Kinetic Energy: Roller Coasters
Student Version
Key Concepts:
Energy is the ability of a system or object to perform work. It exists in various forms.
Potential energy is the energy an object has inside a force field due to its position. In the
roller coaster’s case, the potential energy comes from its height because the Earth’s force
of gravity is acting on it. Roller coasters are able to move their passengers very rapidly up
and down the hills because the cars gain a large amount of potential energy from the very
first hill.
Kinetic energy is mechanical energy that is due to motion of an object.
Thermal energy is energy due to the heat of a system or object. Energy can be converted
to heat through frictional dissipation.
Friction, or frictional dissipation, is a phenomenon in which mechanically useful energy,
such as the motion of the roller coaster, is converted to mechanically useless energy, such
as heat or sound. Friction acts on all moving objects, and it is the reason that a ball rolled
across an open space will eventually slow down and stop.
“Conservation of Energy” is a fundamental principle that energy cannot be created or
destroyed. Rather, it is transferred between different forms, such as those described
above.
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Potential and Kinetic Energy: Roller Coasters

Student Version

Key Concepts:

  • Energy is the ability of a system or object to perform work. It exists in various forms.
  • Potential energy is the energy an object has inside a force field due to its position. In the roller coaster’s case, the potential energy comes from its height because the Earth’s force of gravity is acting on it. Roller coasters are able to move their passengers very rapidly up and down the hills because the cars gain a large amount of potential energy from the very first hill.
  • Kinetic energy is mechanical energy that is due to motion of an object.
  • Thermal energy is energy due to the heat of a system or object. Energy can be converted to heat through frictional dissipation.
  • Friction , or frictional dissipation, is a phenomenon in which mechanically useful energy, such as the motion of the roller coaster, is converted to mechanically useless energy, such as heat or sound. Friction acts on all moving objects, and it is the reason that a ball rolled across an open space will eventually slow down and stop.
  • “Conservation of Energy” is a fundamental principle that energy cannot be created or destroyed. Rather, it is transferred between different forms, such as those described above.

Part 1: Effects of Starting Height

  1. You will have 4 pieces of foam insulation. To start, tape 3 pieces of the foam insulation together.
  2. Tape the beginning of the rollercoaster at around 140 cm higher than the floor.
  3. Tape the slide down 40 cm away from the edge of the wall. (See Diagram 1 for the set-up instructions 1- 3 ) Diagram 1
  4. Have one partner form a hill, with its peak located 1 m away horizontally from the starting point as shown in Diagram 2. Do this by pulling up on the insulation to form the peak of the hill. It is helpful to tape the peak of the hill to a chair leg to hold it steady. As one partner holds it still, have the other partner drop the marble from 60 cm vertical height. Diagram 2 (Note: The potential energy of the marble with mass m that starts at height h is equal to mgh. There is no kinetic energy initially if it starts at rest.) SET UP DIAGRAM: 4 PIECES OF FOAM PIPE INSULATION TAPE FOAM PIPE AT 140 CM TAPE SLIDE 40 CM AWAY ADD TAPE HERE: START= 60 CM PREDICTION DIAGRAM: 1 METER

TAPE HERE:40 CM?

PULL ON IT HERE!

  1. Now, tape down the insulation 90 cm away from the starting point as shown in the diagram below, but keep the hill height the same as the maximum height determined in the previous step. (Note: This should give you a steeper slope.) Diagram 3
  2. If the marble makes it over the hill, then raise the height and retry. If it does not roll over, lower the hill and retry. Repeat this process until the maximum hill height is determined (i.e. the marble nearly stops at the top of the hill.) Record it below: _Maximum steep hill height at 150 cm separation =_________________ Another way energy is dissipated is through the flexibility of the foam, allowing the slide itself to absorb some energy as the marble rides up, and slightly pushes into, the side of the hill. Q5. Why do you think the maximum hill height was different for the steep hill and the gradual hill?
  3. Now, make a loop which, at its tallest point, is the same height as the value recorded directly above. Have a partner hold it in place. See Diagram 4 below: START= 120 CM FRICTION DIAGRAM: 150 CM TAPE HERE:40 CM TAPE HERE:90 CM FROM THE START POINT

Diagram 4

  1. Drop the marble from 120 cm and observe whether it completes the loop. Q6. Does your marble complete the loop? Q7. Describe what you saw, if the marble did not complete the loop.
  2. Try dropping the marble through a loop that is small enough for the marble to get through the highest point. If it does not complete the loop, then lower the loop size until it succeeds. _Actual maximum loop height = _____________________ If an object is to continue through a vertical loop, it is not enough for it to merely reach the highest point of the loop. It must actually have a minimum non-zero velocity (it must be moving) along the track at the top point in order to stay in contact with the loop. This velocity depends on the acceleration due to gravity, g , and the radius of the loop, r : v (^) min= gr
  3. Calculate the radius of your loop. Measure how high your loop is and divide by 2: _Radius = _____________
  4. The acceleration due to gravity is 9.8 m/s 2 (980 cm/s 2 ). Calculate the minimum velocity the marble must have to complete the loop: _Predicted minimum velocity = ________________ START= 120 CM LOOP DIAGRAM: TAPE HERE:40 CM TAPE HERE:90 CM FROM THE START POINT 100 CM= 1 METER150 CM